Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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![The cylindrical coordinate robot on a factory's assembly line is shown in a top view. A force of 65 N acts on a workpiece being held at the end of the robot's arm. The goal is to express the 65 N force as a vector in terms of unit vectors \( \mathbf{i} \) and \( \mathbf{j} \), which are aligned with the \( x \)- and \( y \)-axes.
### Diagram Explanation
In the diagram:
- The robot arm is positioned at a 30° angle from the positive x-axis.
- The force vector \( \mathbf{F} \) is applied at a 70° angle from the robot arm.
### Vector Representation
To express the force vector \( \mathbf{F} \) using \( \mathbf{i} \) and \( \mathbf{j} \), it requires resolving the force into its x and y components:
- The x-component (\( F_x \)) of the force can be calculated with:
\[
F_x = 65 \cos(30° + 70°)
\]
- The y-component (\( F_y \)) of the force can be calculated with:
\[
F_y = 65 \sin(30° + 70°)
\]
### Expression
Express your answer as a vector using the unit vectors \( \mathbf{i} \) and \( \mathbf{j} \).
\[
F = \underline{\hspace{1cm}} \mathbf{i} + \underline{\hspace{1cm}} \mathbf{j} \text{ N}
\]
(Make sure to express your answer using three significant figures.)](https://content.bartleby.com/qna-images/question/480f989f-2af6-48a5-ab4d-ef9ac310c5f5/43080257-bce1-49d8-989f-cfa8901107ff/zjdiei_processed.png)
Transcribed Image Text:The cylindrical coordinate robot on a factory's assembly line is shown in a top view. A force of 65 N acts on a workpiece being held at the end of the robot's arm. The goal is to express the 65 N force as a vector in terms of unit vectors \( \mathbf{i} \) and \( \mathbf{j} \), which are aligned with the \( x \)- and \( y \)-axes.
### Diagram Explanation
In the diagram:
- The robot arm is positioned at a 30° angle from the positive x-axis.
- The force vector \( \mathbf{F} \) is applied at a 70° angle from the robot arm.
### Vector Representation
To express the force vector \( \mathbf{F} \) using \( \mathbf{i} \) and \( \mathbf{j} \), it requires resolving the force into its x and y components:
- The x-component (\( F_x \)) of the force can be calculated with:
\[
F_x = 65 \cos(30° + 70°)
\]
- The y-component (\( F_y \)) of the force can be calculated with:
\[
F_y = 65 \sin(30° + 70°)
\]
### Expression
Express your answer as a vector using the unit vectors \( \mathbf{i} \) and \( \mathbf{j} \).
\[
F = \underline{\hspace{1cm}} \mathbf{i} + \underline{\hspace{1cm}} \mathbf{j} \text{ N}
\]
(Make sure to express your answer using three significant figures.)
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